Motor vehicles commonly include a steering shaft, a manual steering wheel on the steering shaft, and a steering gear which steers dirigible wheels of the motor vehicle in response to rotation of the steering shaft. Power assist apparatuses have been proposed through which manual effort applied at the steering wheel by a driver of the motor vehicle is supplemented by output torque of an electric motor connected to the steering shaft through a speed reducer consisting of a worm gear driven by the electric motor and a worm wheel connected to the steering shaft. Performance of such power assist apparatuses is optimized when lash between the worm gear and the worm wheel is minimized. A power assist apparatus according to this invention for motor vehicle steering is constructed for simple and effective elimination of lash between a worm gear and a worm wheel of a speed reducer of the power assist apparatus.